question_answer

Fifteen persons among whom are A and B, sit down at random at a round table. The probability that there are 4 persons between A and B, is

A)            \[\frac{1}{3}\]                          

B)            \[\frac{2}{3}\]

C)            \[\frac{2}{7}\]                          

D)            \[\frac{1}{7}\]

Correct Answer: D

Solution :

                   Let \[A\] occupy any seat at the round table. Then there are 14 seats available for \[B.\] If there are to be four persons between \[A\] and \[B.\] Then \[B\] has only two ways to sit, as show in the fig. Hence required probability \[=\frac{2}{14}=\frac{1}{7}.\]